An important concern in the study of heat transfer is to determine the steady-state temperature distribution of a thin plate when the temperature around the boundary is known. The figure represents a cross section of a metal beam, with negligible heat flow in the direction perpendicular to the plate. Let T₁. T₁ denote the temperatures at the four interior nodes of the figure. The temperature at a node is approximately equal to the average of the four nearest nodes-to the left, above, to the right, and below. Solve the system of equations below to find the temperatures T₁.... T4- ****** 4T₁ T₂ - T₁=40 =75 T₂ +4T3- T₁=85 - T3 +4T₁=50 -T₁+4T2 T3 - - SCOX 150 150 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The unique solution of the system is . (Type integers or decimals rounded to the nearest thousandth as needed.) B. The system has infinitely many solutions. C. The system has no solution. 25° 25° 1 4 35⁰ 2 3 350 50° 50°

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